I was wondering if there is any research in the field of Diophantine Approximation using the computable numbers. It seems to be a good fit, a dense countable set with a variety of different potential ...

I mean, of course $e^{e^9}$ is not an integer, but can we prove this? If you're thinking of asking Wolfram|Alpha, be warned: it gives different answers to the questions "is exp(exp(9)) an integer" (WA ...

I am representing denominators in rational numbers with powers of their prime factors for easy multiplication and division in lowest terms (by adding and subtracting the prime powers). I would like ...

Consider the lattice $\mathbb{Z}^{n}\subset\mathbb{R}^{n}$ and a line (not necessarily through the origin).
What conditions can be placed on the slope of the line that is necessary and sufficient so ...

Does the sequence $\frac{1}{e^k \sin{k}}$ converge?
If $\sin{k}$ acts as a random variable (taking on values in $(-1, 1)$), then it seems like we should be able to prove that the sequence converges ...

I am not coming from a pure mathematical background, and now in my daily life as an engineering student, I am getting faced to spatial basis functions to approximates variables. The problem is: Are ...

I noticed that diophantine expressions are great to approximate constants or simple functions, as far as I know, they are not so great when it comes to approximate and compute transcendental functions ...

Minkowski's theorem for convex bodies states that every convex, symmetric subset of $\mathbb{R}^d$ whose volume is larger than $2^d$ contains a non-zero integer point. All the proofs I've seen rely on ...

Given a vector of complex number $\vec{z}=(z_1,\cdots, z_n)$ with $|z_i|=1$ and $z_i$ is not a root of unit, and a vector of complex numbers $\vec{r}=(r_1, \cdots, r_n)$ with $|r_i|=1$. Is it the case ...